close

Вход

Забыли?

вход по аккаунту

?

Приложения экспоненциальной аппроксимации по целочисленным сдвигам функций Гаусса.

код для вставкиСкачать
,
2, 2013
517.518.85
.
.
,
.
.
)
–
.
,
-
.
,
.
-
,
.
In this paper we consider approximations of functions using integer shifts of Gaussians –
quadratic exponentials. A method is proposed to find coefficients of node functions by
solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and
uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
:
,
,
,
,
-
.
-
-
.
(
-
,
).
[1-2].
-
[6-8],
,
,
,
.
.
,
-
.
[3-5],
(
).
[1-8].
,
-
.
.
( ),
-
.
,
s > 0,
.
.
( ),
,
-
:
(
( )~
)
.
,
(1)
.
-
-
:
©
90
.,
( ) = ( ),
-
-
., 2013
.
,
(2)
.
,
2, 2013
:
(
( , , )=
)
(3)
.
,
,
-
.
= 0,
:
( , )=
(2)
( , , ).
,
() ( , )=
(4)
( , ),
)=
1,
=
0,
,
=
( ,
, )
,
=0
.
0
( )=
-
.
:
( , )= ( ,
:
:
( , )= ( ,
( )=
( )
=
( ,
(6)
,
,
=
:
(
)
(
)
(
(
)
)
(6)
)
( , , ),
-
(
( ) –
,
(1)):
(
)
(7)
-
–
(4).
,
1,
(6),
(8).
,
,
() ( , )
(
)
-
) = ( ) 1 = ( ).
-
(4):
1
-
(4),
(5).
-
:
(6)
(1),
.
.
-
=
= ,
(6)
:
, )
(1)-(2),
)
)=
)
,
(5),
)
.
(
(5)
.
,
(
=
:
( ,
( ,
()
=
= +
() ( ,
()
=
,
(1).
=
( )=
=
=
:
(
)
,
.
(8)
.
=
,
.
91
,
2, 2013
,
-
.
(
)
=
,
,
(
,
(8)
:
-
,
.
1
1
(8)-(9).
1
1
1
1
1
:
,
= (… ,
,
(
=
,
,
(8),
,
= ( , , ),
= 1,
1.
,
,
,
,
=± ,
2.
).
,
=
=
,
.
,
,…)
,
-
.
-
,
)
(8)
(… ,0, 0, , ,
=
92
,…),
.
.
(9)
3.
[9-10]).
1.
-
(9)
:
=( ,
(
=
)=
2.
(9)
).
.
.
.
(
=
,
(9). (
(9). (
,
,
=
,
-
(9),
,
(
> 0.
(
:
0, < 0
=
.
,
0
.
«
,
(8)
1
(
)(
1)
.
).
1)
(
1) .
0<
,
,
»
……(
(
-
,
,
< 1,
-
.
,
(9)
, … ),
)
,
s> 0
-
,
=
1
1
,
-
).
:
.
=±
=0
n= 2:
,
:
, … ),
,
= (… ,
,
,
)
-
.
,
(9)
.
2 +1
”
»:
=
(9)
.
.
«
)
.
).
,
.
(8)
(
,
(9)
=
(9)
,
,
3.
.
-
,
2, 2013
MATHEMATICA
, .
4.
,
.
. - 2010. , . .
5
-
. 67. - . 107-116.
[
] /
//
13 (68),
,
.
.
, .
.
,
. .
.
. - 2009.-
17/2. - . 89-99.
6
, . .
.
5.
[
.
.
.
".- 2009., . .
7
:
,
,
,
,
-
,
-
"
1 (8).- . 234-311.
[
.
.
] / . .
,
-
//
(
,
.
).
,
,
, . .
8
,
. - 2009.- . 111.
[
,
,
-
.
.
,
]/ . .
//
-
.
.
]/
. .
//
.
.
,
. - 2008. - . 124-126.
9
, . .
[
.
]/
.
,
-
.
//
-
-
"
",
. - 2011. . .
.
10
,
,
. 260-261.
,
1 Lanzara, F. Approximate approximations
from scattered data [Text] / F. Lanzara, V.Maz’ya,
G. Schmidt // Journal of approximation theory. 2007.- 145. - P. 141-170.
2 Maz’ya, V. Approximate approximations
[Text] / V. Maz’ya, G. Schmidt. – Sweden: University of Linköping, 2007 – 350 P.
3 Zhuravlev, M. V. Jacobi theta-functions and
systems of integral shifts of Gaussian functions
[Text] / M. V. Zhuravlev, E. A. Kiselev, L. A. Minin
et al // Journal of Mathematical Sciences, Springer.2011. – V. – 173. - 2. - P. 231-241.
4
, . .
-[
, . .
]/
. .
. //
,
. .
-
,
-
[
]/
.
.
//
-
«
»,
75. .
.- 2011. - . 234-236.
(
).,
-
REFERENCES
1 Lanzara, F. Approximate approximations
from scattered data [Text] / F. Lanzara,
V. Maz’ya, G. Schmidt // Journal of approximation theory. - 2007.- 145. - P. 141-170.
2 Maz’ya, V. Approximate approximations
[Text] / V. Maz’ya, G. Schmidt. – Sweden: University of Linköping, 2007 – 350 P.
93
,
2, 2013
3 Zhuravlev, M. V. Jacobi theta-functions
and systems of integral shifts of Gaussian functions
[Text] / M. V. Zhuravlev, E. A. Kiselev,
L. A. Minin et al // Journal of Mathematical Sciences, Springer.- 2011. – V. – 173. - 2. - P. 231-241.
4 Zhuravlev, M. V. Jacobi theta-functions
and systems of integer translates of Gaussian
functions [Text] / M. V. Zhuravlev, E. A. Kiselev,
L. A. Minin et al // Contemporary mathematics
and its applications. Partial differential equations. - 2010. - T. 67. - P. 107-116.
5 Minin, L. A. On the computational features of interpolation using integer shifts of
Gaussian functions [Text] / L. A. Minin,
S. M. Sytnyk, M. V. Zhuravlev // Scientific statement of the Belgorod State University. - 2009. 13 (68) Issue 17/2. - P. 89-99.
6 Minin, L. A. Inequalities for Jacobi theta
functions [Text] / L. A. Minin, S. M. Sytnyk // Black
earth almanac research. A series of "Fundamental
mathematics." - 2009. - 1 (8.) - P. 234-311.
7 Minin, L. A. Inequalities for the third Jacobi
theta functions [Text] / L. A. Minin, S. M. Sytnyk //
Analytical Methods of analysis and differential
equations (AMADE). Proceedings of the International Conference, Minsk, Belarus. - 2009. - P. 111.
94
8 Minin, L. A. Inequalities for Jacobi theta
functions [Text] / L. A. Minin, S. M. Sytnyk //
Proceedings of the participants of the International
school on geometry and analysis in memory of
N. V. Efimov, Abrau-Durso, Rostov-na-Donu,
Southern Federal University. - 2008. - P. 124-126.
9 Timashov, A. S. Calculation of the characteristics of the signals at their expansion in the
Gaussian function [Text] / A. S. Timashov // Proceedings of the All-Russia scientific - practical
conference "Actual problems of operating systems
and secure communication systems", Voronezh,
Voronezh Institute of the Ministry of Internal Affairs. - 2011. - P. 260-261.
10 Timashov, A. S. Solution of systems of
equations that determine the coefficients of expansion in integer shifts of Gaussian functions
[Text] / A. S. Timashov // Proceedings of the
Eighth All-Russian scientific conference with international participation "Mathematical modeling
and boundary value problems", on the 75anniversary of U. P. Samarin (MMBVP), Samara. - 2011. - P. 234-236.
Документ
Категория
Без категории
Просмотров
6
Размер файла
147 Кб
Теги
целочисленное, сдвигами, функции, приложение, гаусса, аппроксимация, экспоненциального
1/--страниц
Пожаловаться на содержимое документа